JPMorgan Chase CEO Jamie Dimon is scheduled to testify before a Senate committee later this week, the latest in a series of comeuppances in the wake of his firm’s massive trading losses earlier this year. The spectacle will no doubt spark another round of Dimon-bashing among commentators and other observers. In part that’s a just function of the buck stopping at Dimon’s desk, which makes him rightly responsible for what happens on his watch. But it’s hard not to see a lot of the opprobrium directed toward the 56-year-old banker as a backlash against how he was not that long ago hailed as one of the good guys, a wise and grounded financial steward among all those mean 1%-types.

A problem with either characterization—Dimon as Solomonic Financial Seer, Dimon as Evil Banking Boss—is that they’re black and white in a gray world. But a greater problem is that both ways of looking at Dimon reflect a broader, much more serious issue: All of us—journalists, investors, pundits, investment analysts—consistently overestimate the meaningful effect any boss has over his or her company. There are understandable reasons we tend to do this, but far better reasons to stop.

To be sure, CEOs often make a difference, for good or bad. Few doubt that Warren Buffett or Andrea Jung had a major role in (respectively) the success of Berkshire Hathaway and the failures at Avon. But to what extent that success or failure is correlated to their thoughts and actions—as opposed to forces outside their control—is tough to really know. You can think about it in sports terms: The best football team GM can be quickly undone by a weak training staff, the worst can be made to look brilliant for a while by especially confused opponents. Or think about it in statistical terms: Business results, especially those reflecting the goings on at complex companies, suffer from something called the curse of dimensionality: Data points representing input (all decisions and actions, internal and external) are so numerous and interconnected that it’s both very hard to know what matters and, counterintuitively, almost too easy to see patterns where none might exist. The constellation Leo doesn’t really look like a lion; but, given enough clusters of stars, you can see a lion (or a crab or a bull) if you really want to.

Put another way: Large companies employing tens of thousands of people reflect far more than the strategies set and policies established by the guy in charge, no matter how much we want to believe in the all-powerful CEO. And, boy, do we want to believe in such things. As the Nobel Prize-winning psychologist Daniel Kahneman explains in his bestselling book Thinking, Fast & Slow, the human brain evolved to make understanding the world quick and easy, since quick and easy understanding was, for most of our time on the planet, the key to survival. This remains true despite the fact that our perception of the world often doesn’t align with what’s actually happening. And so we fall victim to—in fact, we rely on—a variety of biases and shortcuts that help us come to conclusions that make the world an easier place to navigate. Not least among them is “outcome bias”—sometimes called “hindsight bias”— whereby we judge the wisdom of an action or decision by how things turned out, not by how the choice looked when the person was doing the choosing.

This is not meant to excuse Dimon or JPMorgan Chase. (Full disclosure: From 2006 through 2008 I was hired by JPMorgan Asset Management to lecture about judgment and decision making in the financial arena.) There is clearly a dangerous mixture of overconfidence, carelessness and recklessness in the processes and oversights of the firm’s trading operations that is hard to fathom, with a level of toxicity that’s yet to be determined. But it’s exceedingly tough to know how much of any firm’s overall failures and successes, let alone its individual failures and successes, can be attributed to the boss. Many have tried to figure it out, of course, and Kahneman reviewed a lot of the studies that over the years have tried to tease out the effect of individual bosses and their strategic decisions on corporate results. His conclusion:

CEOs do influence performance, but the effects are much smaller than a reading of the business press suggest … A very generous estimate of the correlation between the success of the firm and the quality of its CEO might be as .30, indicating 30% overlap.

To explain what that overlap means, Kahneman asks us to imagine many pairs of randomly matched companies. In each pair, the two firms are similar, but the CEO of one is better than the other. The question we’re trying to answer is this: Given a .30 correlation between the success of a firm and its CEO, how often in our pairs of companies will we find that the firm with the stronger boss is also the more successful of the two. The answer? “A correlation of .30,” Kahneman writes, “implies that you that you find the stronger CEO leading the stronger firm in about 60% of the pairs.”

That may seem like a strong correlation, except when you consider the result you’d end up with if the relative success of both firms were determined solely by luck. In that case, you’d find the stronger CEO leading the strong firm 50% of the time. In other words, even if we could identify with certainty which CEOs were aces and which were duds, we’d still only have a slightly better than 50/50 shot at predicting how their firms would perform. This should be humbling, whether we’re calling for the heads of CEOS or showering those noggins with praise, because chance has more to do with what happens at most firms than the qualities of the CEO.

Maybe Warren Buffett is a genius, or maybe he’s a very smart guy—with a lot of smart decisions under his belt along with a lot of middling or poor ones—who’s been immeasurably helped by an incredible run of luck over the past 45 years. Don’t snicker: If you went back to 1967 and blindly considered all CEOs of publicly held U.S. companies, you would expect a handful out of them to experience a seemingly ridiculous run of good fortune over the next few decades, much as you would expect a handful to experience horrendous luck. You would also expect observers to treat the especially fortunate CEOs as geniuses and the especially unlucky ones as morons—or worse.

So maybe Jamie Dimon has been arrogant, reckless and careless in the way he’s run JPMorgan Chase—or maybe he’s a pretty smart guy with a reasonable game plan whose firm was humbled by a combination of poor decisions and bad luck, neither one of which can be avoided by any boss. Certainly he can and should be held accountable. That’s one reason CEOs get paid the big bucks—although the relative ineffectuality of C-suite types is the strongest argument that they are paid too much. More to the point, the folks who lauded Dimon a few years ago as some sort of banking saint were without a doubt overstating the case. And there’s a pretty good chance now that the folks who see him as the root of all evil are equally off the mark. There’s no need to feel sorry for him, mind you; dealing with such pressure is another reason CEOs get paid the big bucks. But it is important to remember the role of chance in business if only because a healthy respect for dumb luck might help regulators and corporate boards determine how to prevent catastrophic events in the future. (By recognizing, for example, the inherent flaws in letting banks and their all-too-human employees engage in high-risk trading to the extent that they are currently allowed.)

Holding individuals responsible for all their decisions is one thing. Blaming them for all their outcomes is another.

Gary Belsky, former editor in chief of ESPN The Magazine and ESPNInsider.com, is a bestselling author and media consultant who lectures on sales psychology, behavioral economics and decision making to businesses and consumer groups around the world.

Belsky's latest book is Why Smart People Make Big Money Mistakes—And How To Correct Them: Lessons from the Life-Changing Science of Behavioral Economics.